Unit groups of classical rings
Author(s)
Bibliographic Information
Unit groups of classical rings
（Oxford science publications）
Clarendon Press , Oxford University Press, 1988
Available at / 28 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
est.DC19:512.4/K1482070103414
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Note
Bibliography: p. [350]-365
Includes indexes
Description and Table of Contents
Description
This book draws together four areas of mathematics - ring theory, group theory, group representation theory and algebraic number theory, examining their interplay. The main theme centres on two related problems: Problem A - given a ring R, determine the isomorphism class of the unit group [U]R of R in terms of natural invariants associated with R. Problem B - given a ring R, find an effective method for the construction of units of R. The study aims to convey a comprehensive picture of the current state of the subject. Examples have been included to help the research worker who needs to compute explicitly unit groups of certain rings. A familiarity with basic ring-theoretic and group-theoretic concepts is assumed, but a chapter on algebraic preliminaries is included.
Table of Contents
- Part 1 Introduction: notation and terminology
- assumed results. Part 2 Algebraic units: finiteness of the class group
- the Dirichlet-Chevalley- Hasse Unit Theorem
- existence of real and conjugate independent units
- units in quadratic fields and pure cubic fields. Part 3 The unit group of the integers []: relations between the unit groups
- Dirichlet L-series and class number formulas
- cyclotomic units
- bass independence theorem. Part 4 Multiplicative groups of fields: multiplicative structure of some classical fields
- multiplicative groups of local fields
- intermediate fields
- Kneser's theorem and related results
- fields with free multiplicative groups modulo torsion
- embedding groups
- multiplicative groups under field extensions. Part 5 Multiplicative groups of division rings: commutativity conditions
- subnormal subgroups - preliminary results and main theorems
- periodic multiplicative commutators
- periodic subnormal subgroups
- free subgroups. Part 6 Rings with cyclic unit groups: finite commutative rings with a cyclic group of units: rings with a cyclic group of units - the general case. Part 7 Finite generation of unit groups: general results
- finitely generated extensions
- the Whitehead group and stability theorem
- finite generation of GL n(R). Part 8 Unit groups of group rings: definitions and elementary properties
- trace of idempotents
- units of finite order
- trivial units
- conjugacy of group bases
- torsion-free complements
- units in commutative group rings. (Part contents)
by "Nielsen BookData"
